How does g(t) = 1/2t change over the interval t = 0 to t = 1?

We will determine the inequality as follows:

*First: We will determine the interception point of the two equations, that is:

So:

Now, we replace x = 10 on any of the two equations:

So, the interception point is located at (10, 85).

*Second: We determine the inequality that represents the problem, that is:

[This is overall, the second equation represents greater cost].

*Third: The least number of medals that cab ve ordered so company's A cost is less than company's B cost is 10 medals.

The given cylinder has a height of 7.5 cm and volume of 150 cubic centimeters,

Consider that the volume and base area of a right circular cylinder are related as,

Substitute the values and solve for A,

Thus, the base area of the given cylinder is 20 sq. cm.

Therefore, option b is the correct choice.

In this case, the answer is very simple.

We must perform the division and verify that the result is a whole number.

1000 / 4 = 250 ===> 250 is a whole number

The answer is:

The number is 250 .

Answer:

250, hope this helped my love have a good rest of your day ^^

Step-by-step explanation:

if you simply devide 1000 by 4 then you get 250 wich yes , is indeed a whole number ^^

The slope usually indicates the behavior of a line:

In the above picture there are 3 different lines with different slopes, let's describe them:

-L1. This red line has a positive slope, it means that as "x" increases, then "y" increases as well.

-L2. This blue line has a negative slope, which means that as "x" increases, then the value of "y" decreases.

-L3. This green line is horizontal and has zero slope . This means that it doesn't matter the value of "x", "y" always has the same value.

Using this description, we can now assure that the slope in your graph is NEGATIVE

We will have that the best way to write it in standard form is B, we clear the parentheses and solve for x.

*That is because the function is already factored, and we will combine like terms and equal to 0 in the remaining steps.

The equation of line which shown in graph will be;

⇒ y = 2x

Option 3 is true.

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph for the equation of line is shown in figure.

Now,

Take two points on the line of the graph.

Two points are ( 1, 2) and (2, 4)

Find the slope of the line with two points (1, 2) and (2, 4) as;

⇒ m = (4 - 2) / (2 - 1)

⇒ m = 2 / 1

⇒ m = 2

Thus, The equation of line passing through the points (1, 2) and (2, 4) with slope 2 is;

⇒ y - 2 = 2 ( x - 1 )

⇒ y - 2 = 2x - 2

⇒ y = 2x - 2 + 2

⇒ y = 2x

Therefore,

The equation of line will be;

⇒ y = 2x

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The perimeter can be calculated by adding the legnths off all 4 sides.

Since it is 5 inches wide and 3 inches tall, it has 2 sides of 5 inches and 2 sides of 3 inches. So, the perimeter is:

16 inches.

After factorizing the expression we get the result as -1 and -2/3.

Given,

the expression is:

3x²+5x+2

Multiply the terms and get the factors.

6x²

Now split the numbers according to the term

3x² + 3x + 2x + 2

collect the like terms.

Arrange the like terms.

3x(x+1) + 2(x+1)

re arrange the terms.

(x+1)(3x+2)

now get the value of x:

x+1 = 0

x = -1

or

3x+2 = 0

3x=-2

x=-2/3

Hence the factors of x are -1 and -2/3

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Explanation:

The new figure is a square prism, with the sides that measure 4x5 = 20 cm.

We have to find the surface area of this prism. To do this we have to find the area of the rectangular faces and the area of the base, which is the same as the area of the top. The total surface area is 4 times the area of the rectangular face plus 2 times the area of the base/top.

Answer:

C. 450 cm²

Multiply each side by 10, then simplify

Here, we want to know how to proceed with solving the equation

As we can see, we have the division sign between the terms on the left hand side of the equation

To solve the equation, we have to find the value for x by isolating it

What this mean here is that we will have to multiply both sides by 10; so that we can isolate x

Thus, the correct answer here is to multiply each side by 10, then simplify

Given:

The charge for parking consists of a flat fee of $1.00 and $1.60 per hour.

To find:

a) Write a linear function P(t).

b) Evaluate P(1.4)

Explanation:

a)

Since the flat fee is $1.00 and the varying fee is $1.60 per hour.

So, the linear function of the total cost for parking is,

Where t be the number of hours.

b)

Substituting t = 1.4 in the above function we get,

That means,

The total cost for parking for 1.4 hours is $3.24.

Final answer:

a) The linear function is,

b) The value is,

Conn Math increase by 3 , each week

Conn Sci increase doubling number, every week

Then now fill table

. Week. 1. Conn Math. Conn Sci

. Week 1. 25. 25

. Week 2. 28. 50

. Week 3. 31. 75

. Week 4. 34. 100

Now part. B

A linear model is when data fits in a straight line

hence Then

Then

First model of Conn Math is

Visitors. = 25 + 3 W

Second model for Conn Sci

Visitors = 25 x

The function we have is:

First, we need to find the rate of change of this function and then we can compare it with the rate of change of each option.

To find the rate of change, we compare the given equation with the general slope-intercept equation:

Where m is the slope, also called the rate of change and b is the y-intercept.

By comparing the two equations, we find that the rate of change is:

So now we will analyze the given options to see in which of them we find a rate of change of -1.

Option A:

In this option (and in option B) we have a table of values for x and y.

We calculate the rate of change by taking two (x,y) points from the table,

Here, we will take the first two (x,y) values and label them as follows:

And we calculate the rate of change "m" using the slope formula:

Substituting the values we get:

Solving the operations:

The rate of change if NOT -1, this option is not correct.

Option B. We do the same as in the first option.

Label the first two (x,y) values as follows:

And use the slope formula:

Substituting the values:

Again, the slope or rate of change is NOT -1, this is also not the option we are looking for,

Option C. In options, C and D we have a graph. To find the rate of change from the graph of a line, we take two points where the line passes, and find the rate of change as follows:

For the graph in C, we will take the following red points

Drawing a triangle between the points we can find the change in y and the change in x:

Thus, the rate of change is:

C is the correct option.

Simplify the given expression as shown below

On the other hand,

Solving for y using the special triangle shown below

Thus,

Then,

The two sets of solutions are

Given:

the sequence shown below that starts with n = 1

The rule of the sequence will be as follows"

The first term = 1, when n = 1

The second term = 4 = 2², when n = 2

The third term = 9 = 3², when n = 3

..

..

So, the rule will be:

We are asked to find the surface area of a triangular prism. To do that we must add the areas of each of the faces of the prism, that is, three rectangles and two triangles. The area of each rectangle is:

Solving the operations we get:

Now we find the area of the triangles, knowing that the area of a triangle is the product of its base by its height over two, like this:

The base is 5 cm and the height is 6cm, replacing we get:

Now we add both areas having into account that there are two triangles, like this:

Replacing we get:

therefore, the surface area is 210 square centimeters

We have a feasibility region and we have to find at which point of the region the function P can be maximized:

As this is a linear function, the maximum value will be in one of the vertices of the region. We can identify the vertices as:

We can calculate the value of P for each of the vertices and see which one has a maximum value. We can already guess that P(8,0) will be greater than P(0,8) as the coefficient for x is greater than the coefficient for y.

We can calculate the three values as:

Answer: the maximum value of P is 28.

Answer:

[tex][d(A, B)]^2=\boxed{85}[/tex]

[tex][d(A,C)]^2+[d(B,C)]^2=\boxed{85}[/tex]

[tex]\sf Area=\boxed{17}\; units^2[/tex]

Step-by-step explanation:

From inspection of the given diagram, the vertices of the triangle are:

If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side.  This is the definition of Pythagoras Theorem.

Use the distance formula to find the side lengths of the triangle.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-5))^2+(-2-5)^2}\\&=\sqrt{(6)^2+(-7)^2}\\&=\sqrt{36+49}\\&=\sqrt{85}\end{aligned}[/tex]

[tex]\begin{aligned}d[(A, C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-1-(-5))^2+(6-5)^2}\\&=\sqrt{(-4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\end{aligned}[/tex]

[tex]\begin{aligned}d[(B, C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-1-1)^2+(6-(-2))^2}\\&=\sqrt{(-2)^2+(8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\end{aligned}[/tex]

Therefore:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

The triangle is a right triangle if:

[tex][d(A,C)]^2+[d(B,C)]^2=[d(A,B)]^2[/tex]

Substitute the found side lengths into the formula:

[tex]\implies [\sqrt{17}]^2+[\sqrt{68}]^2=[\sqrt{85}]^2[/tex]

[tex]\implies 17+68=85[/tex]

[tex]\implies 85=85[/tex]

Therefore, this proves that ΔABC is a right triangle.

To find the area of a right triangle, half the product of the two shorter sides:

[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,C)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{17} \cdot \sqrt{68}\\&=\dfrac{1}{2} \cdot \sqrt{17 \cdot 68}\\&=\dfrac{1}{2} \cdot \sqrt{1156}\\&=\dfrac{1}{2} \cdot \sqrt{34^2}\\&=\dfrac{1}{2} \cdot 34\\&=17 \sf \; units^2\end{aligned}[/tex]

Therefore, the area of the given triangle is 17 units².

The graph of solution of system of linear inequality can be obtained by plotting the given equations and and then shading the region according to the inequality sign.

How to graph two linear inequality?

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Observe the given graph carefully.

It is evident that 'b' is the independent variable (representing the number of books read) for the function f(b) (representing the number of points earned).

The domain of a function is the set of all values of the independent variable that lie within the function.

The graph is plotted from x=0 to x=24.

And the number of books cannot be fractional.

So it can be concluded that the domain of the function is the set of whole numbers from 0 to 24. Also, the function is also defined at the end-points. So the set will be inclusive of the end-points 0 and 24.

Therefore, the 2nd option is correct for the first blank.

The domain is a subset of all possible values of variable 'b'. So it will represent the number of books that Jacob reads.

Thus, the 1st option is the correct choice for the second blank.

The correct option is option A

Explanation:

First we solve the inequality:

-7x -13 ≥ 8

collect like terms:

-7x ≥ 8 + 13

-7x ≥ 21

Divide through by -7:

x ≤ 21/-7

Note: when you divde an inequality by negative number, the iequality sign changes.

x ≤ -3

Since x is less than or equal to -3, the number line starts at -3 and moves towards the left of the number line.

The correct option is option A

Step 1:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.

Step 2:

Write the corresponding sides and angles

The angles are not corresponding to the sides

Step 3

Final answer

The two right angles are not the same because the sides and the angles are not corresponding.

Asnwer:

QR = 18

Explanation:

If Point M is the midpoint of segment QR, then the following expressions are true

QM = MR and;

QM + MR = QR

Given

QM = 2x + 5 and MR = 5x – 1,

Recall that QM = MR

2x + 5 = 5x - 1

2x - 5x = -1-5

-3x = -6

x = -6/-3

x = 2

Get the length of QR

QR = QM + MR

QR = 2x+5 + 5x -1

QR = 7x +4

QR = 7(2) + 4

QR = 14+4

QR = 18

Hence the length of QR is 18

ANSWER

$3,450

EXPLANATION

She started the savings account with $3,000.

The simple interest rate is 3% and the number of years is 5 years.

To find the amount of money in the account after 5 years, we have to first find the interest and then add it to the initial amount saved.

Simple Interest on an amount of money (Principal) at a rate R for a number of years T is given as:

Therefore, the interest is:

Therefore, the amount in the account after 5 years is:

Amount = Principal + Interest

Amount = 3000 + 450

Amoun = $3,450

That is the amount in the account.

Solve;

The solution is x = 48

Given points:

(-2,-7) and (5,0)

To get the equation of the line, we will use the formula below:

From the points given

Where

Substituting the values into the equation

simplifying further

The equation of the line is:

The graph of the points (-2,-7) and (5,0) is given below:

The expression is 64 - 1/2 is equivalent to 127/2.

Given,

In the question:

Which expression is equivalent to 64 -1/2

Now, According to the question:

The ex[pression is given as:

64 - 1/2

Find common denominator and write the numerator above common denominator

[tex]= \frac{64 . 2}{2} - \frac{1}{2}[/tex]

Calculate the product or quotient:

128/2 - 1/2

Write the numerator over common denominator:

(128 - 1)/2

= 127/2

Hence, The expression is 64 - 1/2 is equivalent to 127/2.

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Given the function:

The graph of the function is as shown in the figure:

The range of the function will be as follows:

The minimum value of y = 0

And the maximum value of y = 8 (open circle)

So, the range of the function = [0, 8)

To find the total surface area of this cone, we have that the total lateral area is given by the formula:

Where

s is the slant height of the cone, s = 12 inches.

r is the radius of the base of the cone, r = 7 inches.

To that area, we need to add the area of the base of the cone:

That is, this is the area of a circle with this radius. Then, the total surface area is:

Substituting the values in this formula, we have:

Then

Hence, the total area is equal to 417.62 square inches.

The volume of this composite figure is the sum of the volume of the cylinder and the cone.

Volume of Cylinder

The formula is

Where

V is the volume

r is the radius

h is the height

Given,

r = 5

h = 17.8

Substituting, we find the volume:

Volume of Cone

The formula is:

Where

V is the volume

r is the radius

h is the height

Given,

r = 5

h = 6.2

Substituting, we find the volume:

The total volume of the figure is:

1398.01 + 162.32 = 1560.33